Vijay hooked Munaf when the bowler pitched it short for a six over square leg. He later smote the bowler for a lofted four and then two successive sixes over the mid-wicket region with utter disdain.
His belligerence helped the visitors race to 46 in five overs with Plessis playing second fiddle.
A terrible piece of misunderstanding between the Chennai openers helped Mumbai dismiss Plessis when he was sent back by Vijay following a push to mid-on but was beaten by RP Singh's direct hit at the bowler end stumps.
Singh thus made amends for a terrible piece of fielding earlier when he dropped a sitter off Plessis off Munaf Patel.
Chennai then lost Vijay to a piece of indiscreet shot-making. The opener tried a heave Singh when he came back for a second spell and was bowled comprehensively off the fourth ball after the end of power play.
Harbhajan brought himself on into the attack soon after the fall of these two wickets in the space of 9 balls and restricted the run-scoring along with R P Singh.
Super Kings could add only 30 runs between the sixth and tenth overs to be 72 for 2 after ten.
In Image: Chennai Super Kings' Murali Vijay plays a shot